All deism hinges on the definition of deity. Generally, practitioners of religions self-identified as monotheistic rely upon a definition of deity in which there is a single God who created All that Is. The All-that-Is (in this paradigm) includes all matter, all the laws that govern the relationship between bits of matter, all beings (material and immaterial) and all the laws that govern the relationship between those beings. Generally, this God is ascribed several other attributes including being immortal, innatal (unborn and uncreated), omniscient, omnipotent, perfect and good. According to this monotheistic definition of deity anything which is not all these things is not God. Interestingly, the requirement of "good" in this definition of deity opens the door to the existence of a Satan who is everything God is except good, although exactly how two contrary omnipotent beings can exist in the same universe and remain both omnipotent and contradictory is never adequately made clear.

Of course, strictly speaking none of these godly characteristics are required for monotheism. All that is strictly necessary for an individual to be a monotheist is the belief that there is a thing called "God" and that that thing is the unique member of its class. On the other hand, I believe that the definition of "God" needs to be shared by a number of people sharing the same language, but exactly how large that number needs to be is unclear. If I and a bunch of my friends start calling a specific pencil "God", and say that that specific pencil is the only "God", then to what extent does our language match the common usage of the word? I would say that in this case our definition of God is so far from the consensus definition of the word as to be irrelevant if not meaningless.

People who self-identify as polytheistic tend to have a wider variety of definitions of deity than people who self-identify as monotheistic. Nevertheless, the definition of a God or Goddess in a Classical pantheon is an essentially immaterial, immortal being (who may or may not be capable of manifesting in the material of this world) with specific great (certainly superhuman) but not omnipotent powers. Interestingly, all monotheistic world religions have at least admitted the possibility of such beings in their orthodox pantheons except that they have chosen to call them other names: angels, demons, faeries, peri, deva-dasi, djinn, efreet and many many others. Thus, a classical polytheist might regard a monotheist as really being a polythiest in practice, and a monotheist might think that a classical polytheist as really being either an atheist or another monothiest depending on whether the polytheist's pantheon includes a being which matches the monotheist's definition of "God". With the exception of a quibble around the attribute "good" most modern practicing pagans I have met do include such a being in their personal pantheon although they tend to call Her the Goddess. That is, there is quite a lot of commonality between theists despite the indoctrination from both camps that the two positions are supposed to be mutually exclusive.

This reference to the idea of a good God opening the door to the existence of a Satan is perhaps best approached using the old sense of the word "Satan" - Hebrew for adversary. A monotheistic religion may well believe in an opposing force of evil, but will by necessity view it as inferior to God. By contrast, dualistic religions (such as Zoroastrianism) tend to believe that the two gods of good and evil are of equal power, though neither is strictly speaking omnipotent.

While monotheists may believe in the existence of lesser supernatural beings such as angels, and may even accept the existence of entities that are worshiped as gods by others, they will not consider them to be gods. (I'm specifically thinking of C.S. Lewis's Space Trilogy, in which he portrays the members of the Greco-Romanpantheon as angels mistaken for gods by ancient peoples.) The difference is most discernable in the question of worship - Christians and Muslims may believe in angels, but they would consider it a grievous sin to worship one since in their theology only God is worthy of worship.

I'm not qualified to comment on the issue of whether or not Roman Catholics worship saints, so I won't. Maybe some Catholic Everythingian could chime in and explain how they figure in the practice of their faith?